Purpose: This study evaluates the quality of commercial large language model (LLM) machine translation (MT) for Ancient Greek technical prose and benchmarks standard automated MT evaluation metrics against expert human judgment. Design: We evaluated 60 translations by three LLMs (ChatGPT, Claude, Gemini) of 20 paragraph-length passages from 2 works by the Greek physician Galen (c. 129-216 CE): an expository text with two published English translations and a pharmacological text never before translated. Quality was assessed using seven automated metrics and systematic reference-free human evaluation via a modified Multidimensional Quality Metrics (MQM) framework applied by domain specialists. Findings: On the translated expository text, LLMs achieved high quality (mean MQM score 95.2/100). On the untranslated pharmacological text, quality was lower (79.9/100) but bimodally distributed: two passages with extreme terminological density produced catastrophic failures, while remaining passages scored within 4 points of the expository text. Terminology rarity, operationalized via corpus frequency, emerged as the dominant predictor of failure (r = -.97). Automated metrics showed moderate correlation with human judgment only on texts with wide quality variance; no metric discriminated among high-quality translations. Originality: This is the first systematic, reference-free expert human evaluation of LLM translation for any ancient language and the first study identifying textual properties predictive of translation failure.